1. Field of the Invention
The invention relates to an MR method for determining the nuclear magnetization of an examination region, in which the MR signals are acquired along spiral-like trajectories in the spatial frequency domain (spiral-MRI).
2. Description of the Related Art
The invention also relates to a method in which the number of MR data to be measured can be reduced without loss of spatial resolution. As is described in the publication "The k-trajectory formulation of the NMR imaging process . . .", by Twieg, Med. Phys. 10 (5), September/October 1983, pp. 610-621, an MR signal is acquired in the spatial frequency domain or in the so-called k-domain or k-space along a trajectory which is dependent on the temporal variation of the magnetic gradient field activated, after the excitation of the nuclear magnetization in the examination region by one or more RF pulses, until and during the acquisition of the MR signal. The k-domain is a two-dimensional or three-dimensional domain, depending on whether a two-dimensional or a three-dimensional MR examination method is used. The acquisition of the MR signal along spiral-like trajectories offers the advantage of a comparatively fast acquisition of the MR data required for the reconstruction of the nuclear magnetization distribution.
EP-OS 256 779 describes an MR method in which the MR signals are scanned along a spiral-like trajectory in the spatial frequency domain. A problem is encountered in that, because of different relaxation times T.sub.2, the higher spatial frequencies, which correspond to the outer region of the k-domain, are acquired in a different manner, depending on the type of tissue. In order to avoid this problem, redundant scanning takes place in the k-domain during which the spiral-like trajectory is scanned again in the opposite direction or a spiral-like trajectory which has been offset by half the width of one turn is followed in the opposite direction. Such redundant scanning prolongs the examination time and increases the number of MR data to be measured.
The article "High Speed Spiral-Scan Echo Planar NMR imaging-I", by B. Ahn et al., IEEE Transactions on Medical Imaging, Vol. MI-5, No. 1, pp. 2-7, 1986 described a method in which the MR signal in the k-domain is scanned along a spiral whose turns have a distance from one another which amounts to twice the value actually required for the examination of an examination region of a predetermined size and spatial resolution; the measuring time is thus reduced. The missing MR data are derived in the form of MR auxiliary data for auxiliary points in the spatial frequency domain which are situated between neighboring turns of the spiral. The determination of the MR auxiliary data takes into account the MR data measured at points on the spiral which are situated symmetrically to the auxiliary points with respect to the origin point of the spatial frequency domain. However, this method can produce perfect results only if the phase of the MR data is zero. In practice, however, this condition is usually not satisfied. The phase may even exhibit a slight dependency on location.